Don't Be A Tool was launched by two fathers who were horrified by the rising tide of violence on the city's streets and felt traditional tactics being used to steer young people away from gangs were not working.
Two months down the line, its founders are in talks with Sheffield's top sports clubs, including the Blades and the Owls, and already have a number of community groups on board.
Sheffield Wednesday are also working with the campaign's founders on a new programme using football to get the message across to primary school pupils about the dangers of carrying knives.
The club this week hosted the maiden meeting of the Don't Be A Tool steering group at Hillsborough Stadium, bringing together community groups, concerned parents and business and university representatives around the table.
"There's been a lot of hot air in the past. Too often someone will come and give young people a lecture telling them 'this is what you should be doing' and then they're gone," he said.
"We want to up-skill people who are passionate about working with young people in their community and provide them with the support network they need to make a lasting difference."
That means giving them the training, self-belief and connections needed to start their own businesses or find employment, which is why the campaign's founders are keen to link up with as many firms locally and nationally as possible.
"Sometimes you're dealing with people who are generating a fair amount of money through drugs. It's their way of life and how they support their families," said Mr Gibb.
They're young entrepreneurs who might be some of the best business people you've met but unfortunately the business they've chosen is an illegal one which is damaging the communities in which they live.
"We're focusing on that natural talent and giving them an opportunity to replace that life with something they can be proud of."
The campaign's founders hope to sign up 40-50 PALs across the city, who will undergo a two-day training course giving them the skills needed to deliver knife awareness sessions, including basic self-defence techniques.
The PALs will get advice on safeguarding young people from abuse and have access to a 24-helpline and a newly developed app with information about the various activities available to young people in Sheffield.
In the long-term, they will be encouraged to train future community leaders themselves, in a model the founders eventually hope to roll out nationwide.
The aim, say Mr Gibb and Mr Swallow-Gaunt, is to build on the good work already taking place around the city but to get the many individual groups working more closely together and give them the support they need to provide what is needed in their neighbourhoods.
Two of the first groups to get on board are the Friends of Firth Park and the newly-formed organisation Mums United, which was set up by mothers in Sharrow and Nether Edge to tackle crime and anti-social behaviour.
Mums United founder Sahira Irshad said: "I think Don't Be A Tool is brilliant because it's bringing everyone together and helping us learn from each other, which is something that should have been done ages ago.
"Things are really bad and the problems are more deep rooted than people realise. I know of a few mums from other countries who have sent their children back because they're worried about what will happen to them here.
"It's our responsibility to do something as mums and as human beings, and everyone has a role to play, from churches and mosques to the police."
Sarah Hardy, of Friends of Firth Park, said: "We want people to come together, enjoy the park safely and get on with one another, but we know there are knives being stashed in bushes there because we've found them, and it's putting people off using the park.
"In the past you've had people coming to the community and throwing a bit of funding at it without really listening to what people want, but this feels different and everybody's really enthusiastic.
"We're trying to create things which will have a lasting impact and not just fizzle out after six months."
Isobel Dunn, Sheffield Wednesday's Premier League coordinator, said the club was really keen to get involved.
"We see the club as a glue to help create a cohesive community, so we, along with the other clubs in the city, want to do what we can to help," she said.
"Rather than having pupils fall asleep watching a Powerpoint presentation we're going to get them playing football and learning the consequences of their actions through that so hopefully the message sticks."
Don't Be A Tool's founders are looking for potential PALs and are keen to hear from more community groups and businesses in Sheffield. For more information, follow @DontBeATool2 on Twitter or search using the hashtag #DontBeATool.